Rigify/Armature - additional bones cause unwanted deformation
Your ORG-palm.0# finger bones (the base ones) have constraints copying transforms from the ORG-weapon bone.

The constraints were probably targeting different bone originally (hand probably).

Delete those constraints or re-target them to ORG-hand.

Why don't you use Child-Of constraining for picking up objects/weapons? I think you don't need the weapon bone, this seems very non-standard.